Problem: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 8x - 6$ and $ KL = 2x + 24$ Find $JL$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {8x - 6} = {2x + 24}$ Solve for $x$ $ 6x = 30$ $ x = 5$ Substitute $5$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 8({5}) - 6$ $ KL = 2({5}) + 24$ $ JK = 40 - 6$ $ KL = 10 + 24$ $ JK = 34$ $ KL = 34$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {34} + {34}$ $ JL = 68$